Optimal Quadratic Programming and Qcqp Algorithms with Applications
暫譯: 最佳二次規劃與 QCQP 演算法及其應用
Dostál, Zdeněk
- 出版商: Springer
- 出版日期: 2025-10-28
- 售價: $6,890
- 貴賓價: 9.5 折 $6,546
- 語言: 英文
- 頁數: 376
- 裝訂: Hardcover - also called cloth, retail trade, or trade
- ISBN: 3031951662
- ISBN-13: 9783031951664
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相關分類:
工程數學 Engineering-mathematics
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相關主題
商品描述
This book presents cutting-edge algorithms for solving large-scale quadratic programming (QP) and/or by the Hessian's spectrum. While applying these algorithms to the class of QP problems with the spectrum confined to a positive interval, the theory guarantees finding the prescribed precision solution through a uniformly bounded number of simple iterations, like matrix-vector multiplications.
Key concepts explored include the active set strategy, spectral gradients, and augmented Lagrangian methods. The book provides a comprehensive quantitative convergence theory, avoiding unspecified constants. Through detailed numerical experiments, the author demonstrates the algorithms' superior performance compared to traditional methods, especially in handling large problems with sparse Hessian. The performance of the algorithms is shown on large-scale (billions of variables) problems of mechanics, optimal control, and support vector machines.
Ideal for researchers and practitioners in optimization and computational mathematics, this volume is also an introductory text and a reference for advanced studies in nonlinear programming. Whether you're a scholar in applied mathematics or an engineer tackling complex optimization challenges, this book offers valuable insights and practical tools for your work.
商品描述(中文翻譯)
這本書介紹了用於解決大規模二次規劃（QP）問題的尖端演算法，並且涉及Hessian的譜。當將這些演算法應用於譜限制在正區間的QP問題類別時，理論保證通過均勻有界的簡單迭代次數（如矩陣-向量乘法）找到所需精度的解。
探討的關鍵概念包括活躍集策略、譜梯度和增廣拉格朗日方法。這本書提供了一個全面的定量收斂理論，避免了不明確的常數。通過詳細的數值實驗，作者展示了這些演算法相較於傳統方法的優越性能，特別是在處理具有稀疏Hessian的大型問題時。這些演算法的性能在大規模（數十億變數）機械學、最優控制和支持向量機問題上得到了展示。
本書非常適合優化和計算數學領域的研究人員和實務工作者，同時也是非線性規劃的入門教材和進階研究的參考資料。無論您是應用數學的學者還是面對複雜優化挑戰的工程師，本書都提供了寶貴的見解和實用工具，助您在工作中取得成功。
作者簡介
Zdeněk Dostál is a professor at the Department of Applied Mathematics and Senior Researcher at IT4Innovations National Supercomputing Center, VSB-Technical University of Ostrava. Zdeněk works in Numerical Linear Algebra, Optimization, and Computational Mechanics. He published his results in more than 120 papers (Scopus). He is an author of the book 'Optimal Quadratic Programming Algorithms' (Springer 2009) and coauthor of 'Scalable Algorithms for Contact Problems' (Springer 2017) on massively parallel algorithms with theoretically supported linear (optimal) complexity. His current research concerns QP, QCQP, and generalization of the above results to H-TFETI and H-TBETI.
作者簡介(中文翻譯)
Zdeněk Dostál 是捷克奧斯特拉瓦科技大學應用數學系的教授及 IT4Innovations 國家超級計算中心的高級研究員。Zdeněk 的研究領域包括數值線性代數、優化和計算力學。他在超過 120 篇論文中發表了他的研究成果（Scopus）。他是《Optimal Quadratic Programming Algorithms》（Springer 2009）一書的作者，並且是《Scalable Algorithms for Contact Problems》（Springer 2017）的合著者，該書探討了具有理論支持的線性（最佳）複雜度的大規模並行算法。他目前的研究涉及二次規劃（QP）、二次約束二次規劃（QCQP），以及將上述結果推廣到 H-TFETI 和 H-TBETI 的研究。
